Evaluating and Explaining Climate Science

Tropospheric Basics

More on climate basics.. Why is the lower atmosphere – the troposphere – like it is?

Atmospheric Temperature & Pressure Profile, Bigg (2005)

Pressure

The pressure vs altitude relationship is the first point to understand. Notice that (in the graphic above) the left vertical axis – height – is linear, while the right hand corresponding vertical axis – pressure – is logarithmic. Here is one sample atmospheric profile:

Pressure vs Height, Taylor (2005)

As a “conceptual idea” to help understand this, the pressure at any level is dependent on the total weight of atmosphere above. As you go up higher in the atmosphere the weight above decreases. As the weight above decreases, the atmosphere below is less “compressed” due to the pressure and so the pressure change is not linear with altitude. There is some maths at the end for people interested.

Temperature

The temperature decreases with altitude through the troposphere. What explains this?

Firstly, the atmosphere is mostly transparent to solar radiation so the solar radiation passes straight through the atmosphere and is absorbed by the surface – whether land or sea.

Secondly, the surface heats up because of this radiation and consequently warms the lower atmosphere. What we need to understand is the dominant mechanism by which it heats the lower atmosphere.

If we calculate the movement of heat upward through the atmosphere only by radiation (the atmosphere absorbs and emits longwave radiation) we find a vertical temperature profile which doesn’t match what we observe. When the atmosphere is “optically thick”, radiation doesn’t provide a good “re-distribution” of heat. In the troposphere, if radiation was the only mechanism for moving heat, the “lapse rate” – or change of temperature with height – would be more than 10K/km.

As we go up through the troposphere the temperature decreases with altitude. This introduces terminology problems with “more than” and “less than” (especially if we are trying to avoid maths). More rigorously I could say that the temperature change would be less than -10K/km. E.g. -12K/km.

And yet, the actual environmental lapse rate is around -6.5K/km. The “environmental lapse rate” is what we observe in practice.

Now radiation is only one mechanism for moving heat – the others are conduction and convection.

Convection is a very effective mechanism for redistributing heat. The sun heats the earth’s surface (through the almost transparent atmosphere) – the earth’s surface heats the lowest levels of the atmosphere via conduction and convection. What happens to air that is heated? If air heats it expands, and if it expands then its density becomes lower and so it will rise. The first law of thermodynamics – conservation of energy – says that if there is no change in energy then work done by a parcel of air in expanding must equal the change in heat.

This means that for dry air we can easily calculate the temperature change as air rises. The adiabatic lapse rate of dry air is -9.8K/km (=-9.8°C/km).

Calculating the value for moist air is not so simple (but is still basic physics) and depends on the humidity.

First, let’s use the dry lapse rate to consider what might happen in the atmosphere. Suppose the temperature profile has been determined by radiative equilibrium, and is therefore more than 10K/km.

So if the surface is 15°C, then 1km up the temperature will be less than 5°C, and 2km up the temperature will be less than -5°C.

If a parcel of dry air at the surface moves upward 1km then as a result of the change in energy in expanding it will reach a temperature of just over 5°C. It will be warmer than the equilibrium profile that has been established by radiation. This means it will be less dense than the surrounding air and so it will keep on rising.

Therefore, in practice, any dry air which is slightly perturbed vertically will find itself warmer than the surrounding air and will keep on rising.

So convection dominates the temperature profile of the lower atmosphere. If radiative equilibrium dominated, convection would quickly take over – because it is more effective at moving heat in the troposphere (a different story in the stratosphere).

Now let’s consider humid air. As air cools it can hold less water vapor. So water vapor will condense, thereby releasing heat. Therefore, the more humid the air, the warmer it will be at higher altitudes (because of release of latent heat). And so, humid air has a lapse rate which is “less negative” than dry air. This value can be as “low” as -4K/km in the tropics.

And on average the “environmental” lapse rate is -6.5K/km.

Conclusion

Convection determines the temperature profile in the troposphere. But radiation is the only mechanism for moving heat into and out of the earth’s climate system.

It’s common to see “criticisms” on blogs that somehow “climate science has ignored convection and latent heat”. Atmospheric physics 101 always works through these basics to explain the temperature profile of the troposphere.

Convection, latent heat and radiation are all important movers of heat from the surface into the atmosphere. And in the case of radiation, it is also an important mover of heat back to the surface from the atmosphere.

But convection is what determines the actual temperature profile of the lower atmosphere – the troposphere.

Maths of Pressure Changes

To understand pressure vs altitude we use the hydrostatic balance equation.

The change in pressure across a small vertical “slice” of the atmosphere:

dp = -ρg.dz

The ideal gas equation says:

PV = nRT

and

ρ = M/V

so

dp/p = -dz/H, where H is the scale height, or H=RT/mg

Therefore:

H is dependent on temperature and therefore on the altitude, but as a very rough and ready approximation H doesn’t change too much. At the surface H = 8.5km and at the top of the mesosphere, H= 5.8km. The value of H tells us the change in altitude needed to reduce p (pressure) to 1/e (36%) of its original value.

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33 Responses

Yeah- it’s hard not to notice that the temperature profile of the atmosphere is that of a refrigerant system. Phase change doesn’t mess around. Water vapor has a huge volume loss with condensation and it’s the lightest gas as a vapor. It goes to the top and sucks everything else up to fill the gap when it dumps its load of joules for weather.

“Convection, latent heat and radiation are all important movers of heat from the surface into the atmosphere. And in the case of radiation, it is also an important mover of heat back to the surface from the atmosphere.”

Convection does that, too.

Imagine that we took a patch of ground and cooled it below equilibrium, and then left it to see what would happen. The air immediately above it would cool by exchange of sensible heat, and would grow more dense that the air that surrounds it on all sides. This would start a ‘reverse convection’ in which air is drawn downwards over the cold patch and horizontally out over the surrounding land. As air descends, it is compressed, rising in temperature, and continuously warms the ground by sensible heat exchange.

Remember, convection carries heat upwards at the equator, but downwards as one approaches the poles. The polar winter gives six months without the sun, (and even in summer the albedo is high) – without convection mixing things up, how long would it take to radiate all the local heat away?

A temperature inversion blocks convection. For reverse convection to happen, the air would have to cool to a temperature less than the air next to the surface or it would still be less dense than the air next to the surface and would not be drawn downward. Perhaps you mean eddy diffusion, which is much faster than conduction but results in a similar temperature profile. The math describing the planetary boundary layer is very complex. See Chapter 6 of Caballero’s Lecture Note on Physical Meteorology starting on page 142 here: http://maths.ucd.ie/met/msc/PhysMet/PhysMetLectNotes.pdf

NinV- the phenomenon of condensation on the ground below happens all the time it even condenses and freezes.
There are lovely photos of bedewed spider webs and frosted windows are stuff of holiday carols.

I think it is worthwhile to note that this can not happen in a bottle of still or dry air.

Here are some numbers used by people who insulate houses:
Heat through a floor is tranfered by conduction and radiation.
There is zero convection to heat a floor.
Of the heat lost through a floor, because of poor conduction, 99% is lost by radiation.
It has been my practice for over a decade to install a layer of aluminum foil, shiny side up, beneath tile floors which returns 99% of that, . People are amazed to find that the bathroom suddenly has the warmest floor in the house. All that fiberglass under a floor – wasted just to follow convention in most cases.

I think your use of the adiabatic lapse rate to dismiss the significance of convection to heat transport is misguided. The adiabatic lapse rate is the decrease of temperature with altitude for a stationary atmosphere. Heat is often moved upward by convection under non-stationary conditions; thunderstorms and hurricanes come to mind. When the transported molecules emit radiation at the higher altitude, the likelihood that the photons will exit the climate system into space is greater than it otherwise would have been.

The adiabatic lapse rate and the moist adiabatic lapse rate are what initiate and stop convection – it’s not dismissed at all.

Heat moves through the lower atmosphere primarily by convection – which I said in the article:

So convection dominates the temperature profile of the lower atmosphere. If radiative equilibrium dominated, convection would quickly take over – because it is more effective at moving heat in the troposphere (a different story in the stratosphere).

Perhaps “dismiss” was the wrong word, but I don’t see why the fact that heat must ultimately leave the earth’s climate system as radiation in any way rebuts claims that climate science doesn’t sufficiently account for the effect of convection. You can’t simply boil down convection to adiabatic lapse rate and somehow claim that quantifies its effect.

I think the important point is that, on average, the Surface has to get rid of a large amount of energy.

As Science_of_Doom has pointed out, it does this in 3 ways:
1. By direct conduction.
2. By NET radiation. This is a relatively weak mechanism. (eg, have a look at the Kiehl &Trenberth diagram in IPCC WG1 Chapter 1, where the NET radiation is about the same magnitude as Conduction, at around 25W/m^2).
3. By converting liquid water into Water Vapour. This, according to the Kiehl & Trenberth diagram, is around 3 TIMES as fierce as each of the other two mechanisms.

Energy CONDUCTED into the atmosphere enters at the base. Most of the NET absorbed surface RADIATION enters the atmosphere in the lowest 500m or so (working from the standard absorption tables for CO2, but guessing for H2O…). The Latent Heat in Water Vapour seems to be released fairly linearly with air pressure right up to the Tropopause. (I previously thought it must all be released at cloud height, until I had a look at radiosonde measurements).

If the Surface temperature increases, the NET energy transfer by surface radiation DECREASES, this being balanced by an increase in evaporated water. The NET energy transfer to the atmosphere remains the same, but the DISTRIBUTION of that energy is different. (Due to its relatively high temperature, and the mechanism of evaporation, the surface is very insensitive to changes in “forcing”, around 0.095 to 0.15W/m^2).

I hope I have most of that correct.

[OT Where I struggle is what comes next – how the energy beaten into the atmosphere by the surface leaves the atmosphere. My calculations for CO2 emissions show that well over 50% of the emission power to Space is from the Stratosphere – and at Wavenumber 650, over 50% of emissions must be coming from above 45km.
Water Vapour emissions are presumeably from much lower, around the tops of the clouds (but until recently I had been assuming that the Stratosphere has very little water vapour – radiosonde data tells a different story, so some of the water emissions also have to be coming from the Stratosphere).

The problem is the depth of the Tropopause. At the Equator this is small. But elsewhere it is quite thick (the Standard Atmosphere has it from 11 to 20 km), and therefore optically thick. An optically thick Troposphere means very little CO2 emitted energy gets from the Troposphere to the Stratosphere – it can’t make it through. My conclusion is that the Stratosphere outside the tropics is warmed FROM ABOVE.]

DoM, this may seem picky, but I didn’t say “climate science is not accounting for the effect of convection.” In response to your comment,

“It’s common to see ‘criticisms’ on blogs that somehow ‘climate science has ignored convection and latent heat.’ Atmospheric physics 101 always works through these basics to explain the temperature profile of the troposphere.”

I said, “I don’t see why the fact that heat must ultimately leave the earth’s climate system as radiation in any way rebuts claims that climate science doesn’t sufficiently account for the effect of convection. Now, it could be that climate science properly accounts for convection, but discussing of the adiabatic lapse rate and observing that heat must leave the atmosphere as radiation doesn’t refute contrary claims.

I don’t see why the fact that heat must ultimately leave the earth’s climate system as radiation in any way rebuts claims that climate science doesn’t sufficiently account for the effect of convection. Now, it could be that climate science properly accounts for convection, but discussing of the adiabatic lapse rate and observing that heat must leave the atmosphere as radiation doesn’t refute contrary claims.

Allow me to extend my previous comment with an example. One common criticism I’ve seen is that thunderstorms move large amounts of warm air upward, and that because the grid size for long-term GCMs is too course to physically model thunderstorms, their effects can only be roughly approximated through parametrization. Perhaps the parametrization is sufficient, but in certainly can’t be shown by Atmospheric Physics 101.

I asserted above:
“My calculations for CO2 emissions show that well over 50% of the emission power to Space is from the Stratosphere – and at Wavenumber 650, over 50% of emissions must be coming from above 45km.”

Science of Doom asked:
“How did you do your calculations? What was the formula?”

Any photon at 15um has a high chance of being absorbed by a CO2 molecule before it can escape to Space. Only where there are relatively few overlying CO2 molecules will there be significant amounts of 15um photons escaping to Space.

The table for transmission through CO2 at wavenumber 650 has 47.5% survival through 1atmcm at STP. I make 1 atmcm to be approximately the equivalent of 25m of atmosphere at ground level, approximately this is around 0.2% of the atmosphere.

At the other boundary, about the same amount of CO2 (0.2% of the atmosphere) lies above 45km. So in excess of 50% of photons from below that level are being absorbed before they can escape to Space.

The brightness temperature of the CO2 band is about 220 K or just below the the tropopause ~10 kilometers for the 1976 standard atmosphere. Very little radiation is emitted at 45 km. At 45 km looking up, MODTRAN calculates emission intensity from the rest of the atmosphere above that point of 1.2 W/m2. Going to 40 km, it’s still only 1.9 W/m2. It is all from CO2 and ozone, though.

SoD: Apart from issues with GCMs which is a whole different topic, it seems as though you think that climate science is missing something in the role of convection. But I don’t know what it is.

Perhaps I shouldn’t have brought GCMs into the discussion (though in a field like climate science where the output of models is considered evidence, I’m not sure they are a separate topic), but I think my example of thunderstorms is still applicable.

Your explanation seems to suggest that the interaction between radiation and convection is easily understood — Atmospheric Physics 101 — and can be derived from the atmospheric temperature profile. Referring to the adiabatic lapse rate, you say, “This means that for dry air we can easily calculate the temperature change as air rises.” That’s only true in a stationary atmosphere, so it doesn’t extend to, for example, thunderstorms. Your statements that “any dry air which is slightly perturbed vertically will find itself warmer than the surrounding air and will keep on rising,” and “Convection determines the temperature profile in the troposphere” imply a neat, orderly process of gently wafting currents of air that seldom exists in the real atmosphere.

I’m not specifically saying there’s something climate science is missing in the role of convection; I’m saying there are plenty of things missing from Atmospheric Physics 101 in the role of convection.

Perhaps I have given the wrong impression of what atmospherics physics 101 – the troposphere will actually explain.

Convective processes are the major explanation of the temperature profile we see in the atmosphere- not radiative processes.

Perhaps the parallel of pressure in the atmosphere will be useful. The hydrostatic balance equation explains why the pressure profile is roughly logarithmic with height through the atmosphere. But it doesn’t explain why the surface pressure varies from day to day, or why the pressure profile deviates from the logarithmic equation.

The explanation of adiabatic expansion of dry and moist air explains why the atmosphere has an environmental lapse rate of approximately 6.5K/km.

But by itself, it doesn’t explain why the environmental lapse rate varies when it does.

DeWitt Payne stated:
“The brightness temperature of the CO2 band is about 220 K or just below the the tropopause ~10 kilometers for the 1976 standard atmosphere. Very little radiation is emitted at 45 km. At 45 km looking up, MODTRAN calculates emission intensity from the rest of the atmosphere above that point of 1.2 W/m2. Going to 40 km, it’s still only 1.9 W/m2. It is all from CO2 and ozone, though.”

I thank DeWitt Payne for his comments.

The amount of atmosphere above the Tropopause is about 25-30%, taking the Standard Atmosphere as the model, and the base of the Tropopause to be 11km. So any photon coming from there has to successfully pass through 25% of the CO2 before it can escape to Space.

The figures I have for absorption by CO2 at Wavenumber 650 at STP are as follows:
Concentration, atmcm: 0.2/0.5/1/5/10/100
%Transmission: 74/61/48/16/8/0.1

1atmcm is equivalent to 25m of atmosphere at ground level. So half the Wavenumber650 emissions from the Surface are absorbed by CO2 molecules by 25m up from the ground.

At the other boundary, an equivalent amount of CO2 populates the atmosphere above 45km. One would expect a similar attenuation of emissions.

If the measurements show a temperature equivalent to “Just below the Tropopause” this could actually be one of 3 places:
1. Just below the Tropopause (Problem: How does it get through the equivalent of over 100atmcm of overlying CO2 without being heavily attenuated?)
2. Just above the Tropopause (It still has to get through the equivalent of around 25atmcm without being heavily attenuated)
3. Somewhere in the Mesosphere, around 60-70km (Seems very high – too high?)

I prefer option 2. There will be some loss of absorption efficiency in a thin low pressure gas – the wing frequencies will be less attenuated, so the 50% absorption point will be lower. But I cannot see that a frequency which is so fiercely absorbed at ground level will not also be heavily depleted through the final 30% of the atmosphere.

Peak emission to space occurs at the altitude where the transmittance to space is equal to 50%. There is very little absorption above that altitude and emission directly to space decreases rapidly below that altitude (or pressure). Since transmittance is a monotonic function of altitude, there can only be one value of the peak emission altitude. The brightness temperature is a good indicator of the altitude of peak emission. Only a very tiny fraction of radiation at 667 cm-1 is transmitted directly from the surface to space. The observed radiation comes mostly from near the altitude where the transmittance has reached 50% from almost exactly zero at the surface.

I thank DeWitt Payne for his excellent link, and apologise for my tardy reply.
There is a 1970 spectrum from above Guam at http://climateaudit.org/2008/01/08/sir-john-houghton-on-the-enhanced-greenhouse-effect/ There will be other more recent ones, but I haven’t located them.
There is a radiosonde for this location at http://weather.uwyo.edu/cgi-bin/sounding?region=pac&TYPE=TEXT%3ALIST&YEAR=2010&MONTH=05&FROM=1312&TO=1312&STNM=91212 – not the same date, the spectrum is late April, the sonde mid May 40 years on. The sonde shows a thin Tropopause between 16 and 18km at -78DegC.
The spectrum shows a characteristic temperature for most of the CO2 band around -58DegC, but for Wavenumber 670 around -36DegC.
I understand that this characteristic little peak shows up on all spectra.
We know that wavenumber 670 is more fiercely absorbed (the atmosphere is more optically opaque). It follows that it is being emitted higher in the atmosphere than say wavenumber 640. And from the spectrum, higher = warmer.
And that equation is not true below the Tropopause, but is true above the Tropopause.

[…] purposes). Convection and conduction remove the balance of around 100W/m². If you take a look at Tropospheric Basics you can see more about the temperature profile in the troposphere (lower atmosphere) and why […]

[…] of the stratosphere. If you aren’t clear about the troposphere/stratosphere, take a look at Tropospheric Basics. For caveats and explanations about simple models, and about radiation and emissivity, please […]